We recall a powerful tool, the Invariance Principle, originally introduced by Ledrappier [1]}. It was further developed by Avila and Viana, and then also Santamaria [2]}, [3]}.
Kalinin and Sadovskaya developed a version [4]} which allows for direct application to the partially hyperbolic setting with center-bunching and accessibility conditions. More precisely, the principle shows Hölderness of measurable conformal structures invariant under a partially hyperbolic system with suitable accessibility properties.
